Factor and simplify the algebraic expression https://i.gyazo.com/a7909aa9524c6a673dc55292a2e30b32.png
\[(x+3)^{(-1/5)}-(x+3)^{-6/5}\]
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So note that we get \[\frac{ 1 }{ (x+3)^{1/5} }-\frac{ 1 }{ (x+3)^{6/5} }\] by using \[x^{-n} = \frac{ 1 }{ x^n }\]
that's what i don't know how to do
You can simplify it now since we have two fractions \[\frac{ a }{ b } \pm \frac{ c }{ d } = \frac{ ad \pm bc }{ bd } \]
???
It's just algebra at this point
i'm confused with the (x+3)
\[\frac{ 1 }{ (x+3)^{1/5} }-\frac{ 1 }{ (x+3)^{6/5} } \implies \frac{ (x+3)^{6/5}-(x+3)^{1/5} }{ (x+3)^{1/5}(x+3)^{6/5} }\]
It's the same thing if you were using regular numbers
what do I do with the fractional exponents?
What about them
It just wants positive exponents
You can simplify it a bit more if you want
Use your exponent rules for denominator \[x^nx^m = x^{n+m}\]
but isn't it subtraction?
The denominator is being multiplied
can someone explain?
why is the denominator being multiplied?
someone help please
I showed you the algebra rule, that's all I used \[\frac{ a }{ b } \pm \frac{ c }{ d } = \frac{ ad \pm bc }{ bd } \]
b = (x+3)^(1/5) and d = (x+3)^(6/5) please try it yourself
that's exactly the part i don't get. What do I do with the (x+3) raised to the fractional exponent?
Sorry I'm not sure where you're confused
Can you draw it or use equation bar
all I have is \[\frac{ 1 }{ (x+3) }^{1/5}-\frac{1}{(x+3)}^{6/5}\]
oops the exponents are in the denominator
i don't know what to do after that
It's just like fractions the little rule I showed you is just how you do fractions normally, find common denominator and such..
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